The invention relates generally to optical filters and, more particularly, to minimizing loss and ripple in such filters.
Many systems, such as wavelength division multiplexing (WDM), require filters with a relatively flat and smooth-topped spectral response. The prior art has shown that one can construct a filter with a flat spectral response by cascading two waveguide grating routers (WGRs) [1] (Note in this specification, a reference to another document is designated by a number in brackets to identify its location in a list of references found in the Appendix) I focus here on filters that consist of two cascaded gratings, such as waveguide gratings, connected by two or more connecting optical elements, such as waveguides, (which we will sometimes refer to as xe2x80x9cback-to-back gratingsxe2x80x9d), such as shown in FIG. 1. Examples of such filters include wavelength cross connects [2] wavelength equalizers [3], and wavelength add/drops [8].
Such back-to-back gratings do not generally exhibit a flat spectral response, and thus there is a need for providing design criteria for minimizing the loss and ripple in the spectral response through such back-to-back gratings.
In accordance with the present invention, I describe a design technique for minimizing the loss and ripple in the spectral response of an optical filter including one or more gratings, such as waveguide gratings, connected to an array of optical elements. I achieve the smoothest spectral response for a given set of connecting optical elements substantially periodically spaced by a distance xe2x80x9caxe2x80x9d, by choosing the aperture size of the grating to be substantially equal to (fxcex)/a, where xcex is the wavelength of interest and f is the focal length of the grating.